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Journal of the Ramanujan Mathematical Society

Volume 37, Issue 3, September 2022  pp. 273–279.

On the generating matrices of Goppa codes over hyperelliptic curves

Authors:  Giovanni Falcone, Agota Figula and Carolin Hannusch
Author institution:Department of Mathematics and Computer Science, University of Palermo, Via Archirafi, 90123 Palermo, Italy

Summary:  For an (imaginary) hyperelliptic curve H of genus g, we determine a basis of the Riemann-Roch space L(D), where D is a divisor with positive degree n, linearly equivalent to P{1} + … + P{j} + (n − j)Ω, with 0 ≤ j ≤ g, where Ω is a Weierstrass point, taken as the point at infinity. Directly, this provides in turn a generating matrix of a Goppa codes.

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